From the thread title, I thought that perhaps this was going to be a rules question. (Loose impediment or not? How to remove, if movable? Etc.)
By all means, don't go shoveling snow off greens as a matter of agronomy!
From a practical, standpoint, members of your club ought to respond to the problem of snow on greens as follows. Note carefully; do not get any one of these steps out of order.
1. Go into your grill room, tap room or similar establishment.
2. Brew a fresh cup of coffee.
3. Pour coffee into tall coffee mug.
4. Add 1 oz Kahlua® coffee liqueur, 1/2 oz creme de cacao and 1 oz brandy.
5. Top with whipped cream.
6. Sit down with other golfers and discuss crappy weather, plus tour events under way in Hawaii or California.
Note that if you ignore Step 5., there is a possiblity of severe turf damage and injury to golfers.
I'm glad I could help on this important topic.